A345832 - OEIS

%I #6 Jul 31 2021 21:39:39

%S 31251,44547,45827,45892,47667,47971,49572,51092,53316,53476,54531,

%T 54596,54756,57411,58276,58660,59781,59811,59827,59861,59876,59892,

%U 61076,64581,65876,65891,66356,66596,66676,67716,67876,68131,68322,68772,69171,69667,70116

%N Numbers that are the sum of seven fourth powers in exactly ten ways.

%C Differs from A345576 at term 5 because 45907 = 1^4 + 1^4 + 3^4 + 4^4 + 8^4 + 12^4 + 12^4  = 1^4 + 6^4 + 6^4 + 8^4 + 8^4 + 9^4 + 13^4  = 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 11^4 + 13^4  = 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 11^4 + 13^4  = 2^4 + 2^4 + 4^4 + 7^4 + 7^4 + 7^4 + 14^4  = 2^4 + 3^4 + 6^4 + 6^4 + 7^4 + 7^4 + 14^4  = 2^4 + 4^4 + 6^4 + 7^4 + 9^4 + 11^4 + 12^4  = 2^4 + 5^4 + 5^4 + 10^4 + 10^4 + 10^4 + 11^4  = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 9^4 + 14^4  = 3^4 + 6^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4  = 4^4 + 7^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4.

%H Sean A. Irvine, <a href="/A345832/b345832.txt">Table of n, a(n) for n = 1..10000</a>

%e 44547 is a term because 44547 = 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 11^4 + 13^4 = 1^4 + 2^4 + 2^4 + 6^4 + 7^4 + 7^4 + 14^4 = 1^4 + 2^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 1^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4 = 2^4 + 2^4 + 8^4 + 9^4 + 9^4 + 9^4 + 12^4 = 2^4 + 4^4 + 6^4 + 6^4 + 9^4 + 9^4 + 13^4 = 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 11^4 + 12^4 = 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 12^4 + 12^4 = 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 11^4 + 12^4 = 4^4 + 4^4 + 8^4 + 8^4 + 9^4 + 11^4 + 11^4.

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 7):

%o     tot = sum(pos)

%o     keep[tot] += 1

%o     rets = sorted([k for k, v in keep.items() if v == 10])

%o     for x in range(len(rets)):

%o         print(rets[x])

%Y Cf. A345576, A345782, A345822, A345831, A345842, A346259.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021